The Soviet leaders used "scientific socialism" in their propaganda in attempt to convince people that socialism was more progressive than the free market. During the Cold War, science and technology were equated on both sides of the Iron Curtain with progress and the improvement of society. Because of this, each superpower tried to convince the world that its economic system was the "scientific" (and hence forward-looking) one.

Today, the phrase is rare. There is a shortage of Communist propaganda since the collapse of the Soviet Union, and most of the academy's Marxists now describe themselves as "Marxians" and distance themselves from a literal interpretation of Marx's works. Moreover, actual scientists now tend to raise a well-deserved fuss when the word "scientific" is used to describe anything (such as socialism) which does not rest on experimental (not merely philosophical) evidence.

Not a contradiction in terms. Socialism has been accorded scientific treatment by everyone from Marx to Marcuse; it is only when Marx makes prophecies that Marxism becomes unscientific. Scientific, by which I mean grounded on a rigorous system of analysis and not mere "moralizing." By the standards of 20th century empirical science, I'm sure any sort of "premodern" science looks quite sloppy indeed. In addition, Marx's science can be wildly inaccurate; as can any old science be -- Darwinism, for example. Marxian economics is fairly sound, although there a some problems relating to the Labor Theory of Value (which Marx shared with Smith and Ricardo) that have not been worked out yet. Socialism can be as scientific as capitalism; although there are limitations on how scientific economics and sociology can be. (Remember kids, they're only pseudo-sciences.)